Quotient Rule

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$Quotient Rule Example 7$

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$Quotient Rule Example 6$

PJ Chain Rule +Quotient Rule + Simplifying

The Quotient Rule is a formula you can use to find the derivative of a rational function (a fraction). The Quotient Rule formula is

$\frac{d}{dx}\left(\frac{f(x)}{g(x)}\right)=\frac{f'(x)g(x)-f(x)g'(x)}{(g(x))^2}$

To use the Quotient Rule formula, call the numerator of your original function $f(x)$ . Then call the denominator of your original function $g(x)$ . Take the derivative of both functions to find $f'(x)$ and $g'(x)$ .

Start plugging each of these values into the Quotient Rule formula. In the numerator of the Quotient Rule formula, multiply $f'(x)$ by $g(x)$ , then subtract the product of $f(x)$ and $g'(x)$ . In the denominator of the Quotient Rule formula, take the square of $g(x)$ .

Now that you have all of the pieces plugged into the Quotient Rule formula, simplify the new fraction as much as possible, and cancel any terms from the numerator and denominator that you can. The result is the derivative of the original function.

Quotient Rule

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